It is late October, three weeks before the opening of the new Louvre Abu Dhabi, and an atmosphere of purposeful chaos reigns. I am walking through the galleries with the museum’s chief curator, Jean-François Charnier. Accompanying us is a soundtrack of drilling, hoovering and the beeps of reversing vehicles. We pass ancient stone effigies still wrapped in protective plastic sheeting, resembling corpses in a mortuary; we pass a tower of scaffolding where workmen are installing a statue of Rameses, and a wooden box which contains an archer from a sixth-century Damascene frieze. But Charnier is headed for one cabinet in particular, displaying a set of jade axe heads carefully arranged in a group like a shoal of exotic fish.

The axe heads come from north-western France and are about 7,000 years old. Their surfaces and edges are unmarked by wear – these were ceremonial objects and status symbols. But as much as Charnier is interested in what they tell us about stone-age Europe, more intriguing still is how they relate to the items to their right: a series of almost identical pieces which are of equal age but which hail from China. When he was a young archaeologist, Charnier took part in the digs among the megaliths of Brittany which unearthed the French jades. Then he began to study in Paris’s Musée Guimet and discovered their Chinese counterparts. These two cradles of Neolithic civilisation, totally unconnected but making the same objects from the same thing at the same time, seemed to have had a common symbolic language.

The Louvre Abu Dhabi, an offshoot of the famous French museum, is located on Saadiyat island just across the water from the main city. It is dedicated to the threads connecting distant cultures. Billing itself as a “universal museum”, it tells the story of human history through artefacts and artwork ranging from the first known piece of monumental sculpture to the paintings of Yves Klein. Whereas other such museums, like the British Museum or the Met, have separate departments for Greek or Chinese art, this one explores how ideas and art forms have sprung up simultaneously but far apart, and then spread, met and influenced each other. This is a museum about globalisation.

In 12 sections, each exploring a dramatic cultural shift such as the emergence of formalised religion or of the first great powers and containing pieces from diverse corners of the world, the Louvre Abu Dhabi is full of twins and hybrids: there are totems featuring sun symbols made by Buddhists in India and the Maya in Central America; there are stone fragments from the Gulf inscribed with Christian crosses alongside pagan leaves; and there are pots made from Chinese porcelain and decorated with Arabic script written in blue cobalt from the Islamic world. Globalisation, Charnier says, “wasn’t invented in the 1960s, or the 16th century, or by the Romans. It has always been like this.”

The story starts with a building. In 2006 Abu Dhabi’s Tourism and Culture Authority (TCA) asked Jean Nouvel, a French architect, to design a museum. Their plan was to turn Saadiyat, then an empty patch of sand, into a cultural hub, part of a strategy to be less dependent on oil and more on culture and knowledge. Alongside Nouvel’s museum there would be others, designed by Norman Foster, Frank Gehry and Zaha Hadid. Nouvel didn’t know exactly what his building would be for – the Louvre was not yet involved – but he knew what it would look like. Inspired by the small houses of Arabic medinas and the shade of palm trees in a desert oasis, he designed a set of low, white gallery buildings covered by an enormous dome made from a delicate web of steel and aluminium, its pattern drawing on the geometry of mashrabiya, the latticework of traditional Islamic architecture.

The following year, the Emiratis signed a deal worth more than $1bn with the French government. It gave them a 30-year licence to use the Louvre’s name, to draw on its expertise and to borrow from its collection. It also gave them access to the collections of 12 other French institutions belonging to a new organisation, Agence France-Muséums. Abu Dhabi created an acquisitions fund, to be managed by the Louvre. The deal was controversial – the Louvre was accused of selling out – and the project has been much delayed. Scheduled to open in 2012, it was set back first by the financial crash in 2008 and then by Abu Dhabi’s loan of $20bn to Dubai to help with its debt crisis. Of the other planned museums, only Foster’s – the Zayed National Museum – has even been fully designed, let alone built.

Political divisions haven’t helped. In 2013 Libération, a left-wing French newspaper, published leaked letters from Sheikh Sultan bin Tahnoun al-Nahyan, the TCA’s then chairman, to Henri Loyrette, then the director of the Louvre. He accused the French of being arrogant, was concerned that the money for new acquisitions was being misspent and ordered an audit of the collection. In 2014, the museum held a preview show in Paris which was worryingly incoherent. The exhibits, from Roman statuary to paintings by Cy Twombly, were strong in themselves. But there was no clear idea of how they went together.

The narrative of common humanity now unites them. At times it tips over into corniness – most notably with a poem by Ben Okri, about the many becoming one, which was commissioned for the opening. But the quality of the exhibits, including Leonardo da Vinci’s painting “La Belle Ferronnière” (c.1490), outweighs the sentimentality of the marketing. And although the theme’s breadth could lead to confusion, the neatness of Charnier’s juxtapositions helps maintain intellectual clarity. Adjacent objects are separated by geography, but Charnier has been careful with chronology so that visitors aren’t leaping about in time as well as space. Unlike the jumbled previews, the collection makes visually coherent comparisons: a cabinet of gold masks from Egypt, China and pre-Columbian South America, say, or bronze banquet urns of the same shape from fifth-century China and Greece, which were found in aristocratic tombs. Charnier also has a gift for innovative display. In a room dedicated to coinage (“everyone is bored by coins,” he says) he mounts the money on several layers of glass. When a light comes on, it creates a kaleidoscopic tower of cold, hard cash, which is beautiful to look at whether or not you’re interested in the currency of ancient Cappadocia.

As well as the art, there is the architecture, which is reason in itself to visit. Nouvel’s building, which juts out into the sea, is a masterpiece of light and water. During the day sun streams through the dome, the light puddling on the stone floor and the white buildings. As the sun moves so too does the blue of the water reflected in the grey steel. Outside Nouvel has designed what he calls a “concrete beach”, steps leading to the sea for people to sit on when the weather is cool enough. Inside, he has done the same, and built platforms out in the water for performances. This is a civic space as much as a cultural one, a place for people to hang out whether or not they go to the galleries. Its power is metaphorical as well as visual. Visitors may arrive in buses and cars rather than caravans, but like a stand of date palms in the desert it is a place for meetings of the kind that produced the art inside.